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Many articles that I came across use volume time $v$ in their computations since the market activity level varies substantially throughout the day (intraday volume and volatility patterns), which is the cumulative volume function defined by $v=0$ at the open and $v=1$ at the close.

Could anyone explain the purpose of introducing such a variable? What's the problem with a varying volume profile?

Thanks

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There is a good and a bad point in using volume-time in place of calendar-time:

  • on the one hand, you obtain a more "regular" time series
  • but on the other hand, you cannot synchronize two time series this way: what is the the "common volume time" between two stocks?
  • I am more familiar with the intraday aspect of re-timing than with the daily data. So let me underline that on intraday, you would like to have some "rendez-vous points" that are the same each day, and calendar clock-driven. Some call auctions for instance, or the opening of US market for European stocks.

I would hence say that volume-time is interesting for a narrow "one instrument focus" study. As soon as you want to relate the dynamics of your stock with respect to the "external world" (either a physical clock, or other stocks or any other tradable instrument): you usually have to come back to calendar-time...

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